At 07:42 PM 7/30/2005, Kirby Urner wrote: > > Well, if we are going to split hairs, it's "phee", > > but who cares! > > > >In English we say fie, as in fee FIE foe fum.
My dictionary says otherwise.
> > The two roots (actually, halves of the two > > roots, if I recall correctly) generate the Fibonacci > > sequence. > >The phi sequence is both geometric and recursively additive. > >The usual thing we do with the Fibonacci sequence is show how the ratio >(F[n+1]/F[n]) --> phi as n --> infinity, where F[n+1] and F[n] are >successive terms in this series.
No, no, Kirby. Look at the sequence f1^n+f2^n. Every recursively-generated sequence has a generating polynomial. f1 and f2 are the two roots.
>Math-through-storytelling: part of what we're doing is passing on a >history, a "where we've been" story. It's not like history is >irrelevant. On the other hand, phi to this day has geometric importance >-- its value undimished with time (like gold).
Weeellll... It's a stretch. We no longer build Parthenons.
>phi is an idea and is irreplacable.
In itself--yes. But not in the curriculum.
>I'd think phi, pi and e we could at least agree on, though we might take >different approaches in introducing them.
These are not in the same category. One is essential at an elementary level, the other--a bit later. The third is a mere curiosity--a bump on a path to knowledge.
>It's implicit in writing curriculum that one is saying something like >"follow me" -- and then only some do, maybe none. That's a given.
Really? You obviously are not a member of Mathematically Erect. Also, see the comment about mx+b above--the notation became a convention because it was used in a popular book, not because it has any meaning or convenience.
>However, within the rhetorical conceit of offering leadership, it behooves >me to be persuasive, to exercise whatever leadership experience and >qualities I possess.
If at first you don't succeed, try and try again...
>So: NCLB people, listen up, we're going to push Phi (FIE) and we're going >to do it in connection with solving a Polynomial. This will provide >positive reinforcement for (a) the quadratic formula (b) completing the >square, plus it'll lead to connected topics such as: Fibonacci numbers, >sequences, and five-fold symmetry ala pentagons.